HJB equations in infinite dimensions under weak regularizing properties

详细信息    查看全文

• 作者：Federica Masiero
• 刊名：Journal of Evolution Equations
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：16
• 期：4
• 页码：789-824
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Analysis;
• 出版者：Springer International Publishing
• ISSN：1424-3202
• 卷排序：16

文摘

We solve in mild sense Hamilton Jacobi Bellman equations, both in an infinite dimensional Hilbert space and in a Banach space, with Lipschitz Hamiltonian and Lipschitz continuous final condition, and asking only a weak regularizing property on the transition semigroup of the corresponding state equation. The results are applied to solve stochastic optimal control problems; the models we can treat include a controlled stochastic heat equation in space dimension one and with control and noise on a subdomain.